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The Brownian diffusion of micron-scale inclusions in freely suspended smecticA liquid crystal films a few nanometers thick and several millimeters indiameter depends strongly on the air surrounding the film. Near atmosphericpressure, the three-dimensionally coupled film/gas system is well described byHughes/Pailthorpe/White hydrodynamic theory but at lower pressure (p < 70torr), the diffusion coefficient increases substantially, tending in highvacuum toward the two-dimensional limit where it is determined by film size. Inthe absence of air, the films are found to be a nearly ideal physicalrealization of a two-dimensional, incompressible Newtonian fluid.

Experimental Realization of an Incompressible Newtonian Fluid in Two Dimensions